We want to determine the correlation between the height (in inches) and scoring average (points per game) of women on a college basketball
team. To do this, we record the height and scoring average of two players on the team. The values are
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Let's call the first player "Player A" and the second player "Player B". We have recorded their height (in inches) and scoring average (points per game). To determine the correlation between these two variables, we can follow these steps:
1. Input the recorded values into a spreadsheet or statistical software program. Create two columns labeled "Height" and "Scoring Average". Enter the corresponding values for Player A and Player B in the rows below the respective columns.
2. Calculate the mean (average) for each variable. Add up all the height values and divide by 2 (since we have data for 2 players) to find the mean height. Similarly, add up all the scoring average values and divide by 2 to find the mean scoring average.
3. Subtract the mean from each height value (in the "Height" column) to get the deviation from the mean for each player's height.
4. Subtract the mean from each scoring average value (in the "Scoring Average" column) to get the deviation from the mean for each player's scoring average.
5. Multiply the deviation from the mean for height of Player A with the deviation from the mean for scoring average of Player A. Then, multiply the deviation from the mean for height of Player B with the deviation from the mean for scoring average of Player B. Add these products together.
6. Square the deviation from the mean for height of Player A and the deviation from the mean for scoring average of Player A. Then, square the deviation from the mean for height of Player B and the deviation from the mean for scoring average of Player B. Add these squared values.
7. Divide the sum of the products (calculated in step 5) by the square root of the product of the sum of the squared deviations (calculated in step 6) for both variables.
The result will be a correlation coefficient between -1 and 1, indicating the strength and direction of the relationship between height and scoring average. A positive correlation coefficient indicates a positive relationship (as one variable increases, the other also tends to increase), while a negative correlation coefficient indicates an inverse relationship (as one variable increases, the other tends to decrease).